基于频响函数的网架结构损伤诊断方法研究
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摘要
近几十年来,网架结构作为大跨度建筑结构常用的一种结构形式已经被广泛的应用于工业和民用建筑中,由于受外部载荷、环境作用、灾害、人为等因素的影响,网架结构在服役期间会出现损伤,结构性能下降,其安全性已经引起人们的高度重视。如何去诊断网架结构的损伤,对其健康状况进行诊断和监测,已成为当今亟待解决的一个重要课题,重大建筑物健康监测与损伤诊断也被列为国家科技支撑计划的一个重点科研项目。
相对结构的静力反应来说,结构的动力反应能够更加全面的反映结构的力学物理特性,因而基于振动的损伤诊断方法已成为许多学者的研究热点,并提出了许多损伤诊断方法。然而,这些方法中大部分都需基于模态分析,以模态参数作为损伤识别的基础。由于受到噪声、结构自身特性及人为因素等的影响,用从网架上实测得到的频响函数进行模态拟合时会产生较大的误差,且目前的动测手段只能测得网架的前几阶模态,模态数据不完整,这使得基于模态参数的损伤识别方法应用于网架的损伤识别时无法达到预期的效果。相对模态参数来说,频响函数更直接,误差小,含有更丰富的原始数据信息,且能包含所有的模态参数信息,为此,本文以频响函数作为网架损伤识别的特征参数,应用多元统计分析中的一些基本理论,建立了基于频响函数的网架结构损伤诊断方法,并通过实验室足尺模型网架的动测试验,对提出的方法进行了验证分析,证明了所提出方法的可行性及可靠性。概况起来,本文主要取得的研究成果和得出的结论如下:
(1)通过对频响函数基本概念和物理意义的分析,建立了以频响函数数据为基础,能够包含网架全部模态参数信息的原始数据矩阵,进而构建了损伤识别矩阵,它被作为网架损伤识别的基础。
(2)由于实测频响函数的数据量巨大,所构成的损伤识别矩阵为高维矩阵,因而本文把多元统计分析中主元(主成分)分析和多元控制理论应用于网架的损伤识别中,建立了网架结构的损伤定位方法。首先,运用主元分析方法计算损伤识别矩阵的各阶主元,根据各阶主元的贡献率,找到能包含损伤识别矩阵绝大部分信息的前几阶主元,实现对损伤识别矩阵的降维压缩。然后,运用多元控制图对降维后的矩阵元素进行分析,分离异常数据,提取网架的损伤信息,从而实现对网架结构的损伤定位。
(3)运用多元统计分析中主元分析和马氏(Mahalanobis)距离的基本原理建立了基于频响函数的网架结构损伤程度的评估方法。用网架损伤前后的频响函数建立原始数据矩阵,通过主元分析对原始数据矩阵进行降维、压缩,计算网架损伤前后主元数据间的损伤距离,用网架的整体损伤距离对网架损伤程度进行评估。该方法还解决了本文所提出的网架损伤定位方法对多杆损伤不敏感的问题,弥补了损伤定位方法的不足。
利用无损网架两次实测的频响函数数据,可计算得到网架的最小损伤距离。最小损伤距离是网架出现损伤的最小界限距离,可用于快速的判断网架是否出现了损伤,在网架的在线健康监测中,用于快速的发现损伤,发出预警。另外,最小损伤距离还被作为对网架损伤程度进行评估的基本量值单位。
(4)从实际网架动测中得到的信号都受到噪声的污染,在役网架由于有着复杂的边界条件,质量、阻尼较大,激励响应不够充分等,降低了动测信号质量,为此本文在前人研究成果的基础上,研究了基于主元分析的网架实测频响函数的降噪、消噪方法。通过对网架实测频响函数所构成的原始数据矩阵进行主元分析,利用能包含原始数据主要信息的前几阶主元,重构原始数据矩阵,实现对原始数据的降噪、消噪,为网架的损伤识别提供了可靠的数据保证。
(5)为了验证所提出的损伤识别方法,在实验室完成了足尺模型网架在20种不同损伤工况下的动测试验,通过试验结果分析,证明了所提出的损伤识别方法是可行性、可靠的。同时,对采用力锤激励单输入单输出(SISO)的动测方法及动测中测点布置、激励信号的控制、响应信号的采集、处理、信号的质量评价等进行了较全面的研究、探索,并总结出了一套用冲击力锤人工激励方式进行网架动测的基本方法、步骤。
本文提出的网架损伤诊断方法可直接利用实测频响函数进行损伤识别,不需要模态参数,不要求有完整的模态测试数据,因而避开了实际动测时一些模态参数的测不准及实测模态不完整问题。损伤识别过程是通过分析实测频响函数的数据特征、数据结构来完成,不需建立网架的力学模型,因而对网架的结构形式、约束方式及边界条件均没有特殊的要求,采用力锤人工激励及SISO的动测方法,激励设备简单,操作方便。因而本文提出的损伤诊断方法对于在役网架的健康监测和损伤诊断具有较高的理论价值和实用价值。
In the past several decades, the truss structure has been widely used as an important structure form for large span building. The truss structure of long-term using may be damaged by load effect, ambient factors, natural calamities and incidents, its loading capability will decrease gradually, and its security has attracted people attention. Therefore, it is an imperative problem to detect truss damages so that its security can be evaluated and monitored nowadays. As a results, the health monitoring and damage diagnosis for large structure have been regarded as a key science and technology project for China.
Compared with the response of structure static force, the response of structure dynamic force contains more structure dynamic character, so the damage diagnosis methods based on vibration have become a research focus for many scientists, and many methods have been proposed by them in the past years. However, the most of these methods are based on the modal analysis, and modal parameters are regarded as the basic variables of damage detection. Since the effect of the noise, structural non-linear and artificial factors, etc, some errors will arise from modal analysis when modals are fitted using measured frequency response functions (FRF). Moreover, since we can only obtained partial data of whole modal using current test method, testing data are not integrated, therefore it is difficult for truss damage diagnosis using the method based on modal analysis. Considering the reason given above, a damage diagnosis method based on measured FRF and principal component analysis (PCA) is brought forward in the paper. By means of theory analysis and deduction, the basic theory and method for truss damage diagnosis are formed, and by dynamic experiment of a whole size truss in the laboratory, the proposed method is validated. The experimental result shows that the proposed method is feasible and reliable for truss damage identification. In brief, main research achievements and conclusions in the paper are as follow:
(1) By means of basic concept and practical meaning of FRF, original data matrix, which contains the most of truss modal information, is formed based on measured FRF. Thus, using original data matrix we can constitute the damage identification matrix, which is the basis for truss damage identification.
(2) Since measured FRFs contain large numbers of data, and damage identification matrix has numerous dimensions, a damage orientation method, based on PCA and multivariate control theory, is proposed for truss damage identification. With PCA technology, each principal component of damage identification matrix can be obtained. Then the first several order principal components, which contain the almost all information of damage identification matrix, can be obtained by means of the contribution ratio of each principal component, and the data of damage identification matrix can be reduced. Thus, by analyzing the data character of first several principal components, separating singular data and extracting truss damage information, truss damage elements can be oriented successfully.
(3) Using the Mahalanobis Distance theory of Multivariate Statistical Analysis, an evaluation method for truss damage extent is proposed based on the damage distance. Original data matrix is formed using measured FRFs of undamaged and damaged truss, and its dimensions are reduced with PCA technology. By constituting observation sample using principal component data, calculating the distance between damaged samples and undamaged samples, truss damage extent can be evaluated successfully. At the same time, some problems, which can not be solved very well only using the damage orientation method, also be solved using the damage distance mothed, so damage distance method is a very good supplement for truss damage orientation method.
Using twice measured data of the FRFs from undamaged truss, the minimal damage distance can be obtained. The minimal damage distance is a index for quickly judging truss damage in truss on-line health monitoring. In the other hand, the minimal damage distance can be used as a quantity unit for truss damage extent evaluation.
(4) The dynamic test signals obtained from practical truss have been contaminated by the noise, and existing truss has complicated boundary condition, big mass and damp, so the reliability of dynamic test signal noise is reduced. Therefore, a method for reducing or eliminating FRFs noise is proposed based on the PCA in the paper. By analyzing the PCA of original data matrix, we can reconstruct original data matrix using first several principal components, which generally contain all most information of original data. Thus, the original data noise can be reduced or eliminated, which is the basis for next damage identifications.
(5) In order to validate the reliability of the method, a whole size truss was tested with 20 kinds of damage case. The experimental result shows that the proposed method is feasible and reliable for truss damage identification. At the same time, the measurement points selection, exciting signal control and response signal collection, are also searched for the SISO dynamic test method, as well as testing process and result evaluation. In the last, the basic dynamic test methods and process with manual exciting manner are suggested and summarized in the paper.
The damage diagnosis method proposed in the paper directly uses FRFs for truss damage identification, does not need any modal parameters and integral modal data, so damage diagnosis results are not affected by modal errors and incomplete data. Since the damage diagnosis, which is performed by analyzing FRF data character, does not need truss mechanics mode, so it has not any special requirement for truss structure types, restricting manner and boundary condition. And the dynamic test method using manual excitation and SISO is simple and convenient. Therefore, the damage diagnosis method proposed in the paper has very important theoretical and practical value for health monitoring and damage diagnosis of existing truss.
相对结构的静力反应来说,结构的动力反应能够更加全面的反映结构的力学物理特性,因而基于振动的损伤诊断方法已成为许多学者的研究热点,并提出了许多损伤诊断方法。然而,这些方法中大部分都需基于模态分析,以模态参数作为损伤识别的基础。由于受到噪声、结构自身特性及人为因素等的影响,用从网架上实测得到的频响函数进行模态拟合时会产生较大的误差,且目前的动测手段只能测得网架的前几阶模态,模态数据不完整,这使得基于模态参数的损伤识别方法应用于网架的损伤识别时无法达到预期的效果。相对模态参数来说,频响函数更直接,误差小,含有更丰富的原始数据信息,且能包含所有的模态参数信息,为此,本文以频响函数作为网架损伤识别的特征参数,应用多元统计分析中的一些基本理论,建立了基于频响函数的网架结构损伤诊断方法,并通过实验室足尺模型网架的动测试验,对提出的方法进行了验证分析,证明了所提出方法的可行性及可靠性。概况起来,本文主要取得的研究成果和得出的结论如下:
(1)通过对频响函数基本概念和物理意义的分析,建立了以频响函数数据为基础,能够包含网架全部模态参数信息的原始数据矩阵,进而构建了损伤识别矩阵,它被作为网架损伤识别的基础。
(2)由于实测频响函数的数据量巨大,所构成的损伤识别矩阵为高维矩阵,因而本文把多元统计分析中主元(主成分)分析和多元控制理论应用于网架的损伤识别中,建立了网架结构的损伤定位方法。首先,运用主元分析方法计算损伤识别矩阵的各阶主元,根据各阶主元的贡献率,找到能包含损伤识别矩阵绝大部分信息的前几阶主元,实现对损伤识别矩阵的降维压缩。然后,运用多元控制图对降维后的矩阵元素进行分析,分离异常数据,提取网架的损伤信息,从而实现对网架结构的损伤定位。
(3)运用多元统计分析中主元分析和马氏(Mahalanobis)距离的基本原理建立了基于频响函数的网架结构损伤程度的评估方法。用网架损伤前后的频响函数建立原始数据矩阵,通过主元分析对原始数据矩阵进行降维、压缩,计算网架损伤前后主元数据间的损伤距离,用网架的整体损伤距离对网架损伤程度进行评估。该方法还解决了本文所提出的网架损伤定位方法对多杆损伤不敏感的问题,弥补了损伤定位方法的不足。
利用无损网架两次实测的频响函数数据,可计算得到网架的最小损伤距离。最小损伤距离是网架出现损伤的最小界限距离,可用于快速的判断网架是否出现了损伤,在网架的在线健康监测中,用于快速的发现损伤,发出预警。另外,最小损伤距离还被作为对网架损伤程度进行评估的基本量值单位。
(4)从实际网架动测中得到的信号都受到噪声的污染,在役网架由于有着复杂的边界条件,质量、阻尼较大,激励响应不够充分等,降低了动测信号质量,为此本文在前人研究成果的基础上,研究了基于主元分析的网架实测频响函数的降噪、消噪方法。通过对网架实测频响函数所构成的原始数据矩阵进行主元分析,利用能包含原始数据主要信息的前几阶主元,重构原始数据矩阵,实现对原始数据的降噪、消噪,为网架的损伤识别提供了可靠的数据保证。
(5)为了验证所提出的损伤识别方法,在实验室完成了足尺模型网架在20种不同损伤工况下的动测试验,通过试验结果分析,证明了所提出的损伤识别方法是可行性、可靠的。同时,对采用力锤激励单输入单输出(SISO)的动测方法及动测中测点布置、激励信号的控制、响应信号的采集、处理、信号的质量评价等进行了较全面的研究、探索,并总结出了一套用冲击力锤人工激励方式进行网架动测的基本方法、步骤。
本文提出的网架损伤诊断方法可直接利用实测频响函数进行损伤识别,不需要模态参数,不要求有完整的模态测试数据,因而避开了实际动测时一些模态参数的测不准及实测模态不完整问题。损伤识别过程是通过分析实测频响函数的数据特征、数据结构来完成,不需建立网架的力学模型,因而对网架的结构形式、约束方式及边界条件均没有特殊的要求,采用力锤人工激励及SISO的动测方法,激励设备简单,操作方便。因而本文提出的损伤诊断方法对于在役网架的健康监测和损伤诊断具有较高的理论价值和实用价值。
In the past several decades, the truss structure has been widely used as an important structure form for large span building. The truss structure of long-term using may be damaged by load effect, ambient factors, natural calamities and incidents, its loading capability will decrease gradually, and its security has attracted people attention. Therefore, it is an imperative problem to detect truss damages so that its security can be evaluated and monitored nowadays. As a results, the health monitoring and damage diagnosis for large structure have been regarded as a key science and technology project for China.
Compared with the response of structure static force, the response of structure dynamic force contains more structure dynamic character, so the damage diagnosis methods based on vibration have become a research focus for many scientists, and many methods have been proposed by them in the past years. However, the most of these methods are based on the modal analysis, and modal parameters are regarded as the basic variables of damage detection. Since the effect of the noise, structural non-linear and artificial factors, etc, some errors will arise from modal analysis when modals are fitted using measured frequency response functions (FRF). Moreover, since we can only obtained partial data of whole modal using current test method, testing data are not integrated, therefore it is difficult for truss damage diagnosis using the method based on modal analysis. Considering the reason given above, a damage diagnosis method based on measured FRF and principal component analysis (PCA) is brought forward in the paper. By means of theory analysis and deduction, the basic theory and method for truss damage diagnosis are formed, and by dynamic experiment of a whole size truss in the laboratory, the proposed method is validated. The experimental result shows that the proposed method is feasible and reliable for truss damage identification. In brief, main research achievements and conclusions in the paper are as follow:
(1) By means of basic concept and practical meaning of FRF, original data matrix, which contains the most of truss modal information, is formed based on measured FRF. Thus, using original data matrix we can constitute the damage identification matrix, which is the basis for truss damage identification.
(2) Since measured FRFs contain large numbers of data, and damage identification matrix has numerous dimensions, a damage orientation method, based on PCA and multivariate control theory, is proposed for truss damage identification. With PCA technology, each principal component of damage identification matrix can be obtained. Then the first several order principal components, which contain the almost all information of damage identification matrix, can be obtained by means of the contribution ratio of each principal component, and the data of damage identification matrix can be reduced. Thus, by analyzing the data character of first several principal components, separating singular data and extracting truss damage information, truss damage elements can be oriented successfully.
(3) Using the Mahalanobis Distance theory of Multivariate Statistical Analysis, an evaluation method for truss damage extent is proposed based on the damage distance. Original data matrix is formed using measured FRFs of undamaged and damaged truss, and its dimensions are reduced with PCA technology. By constituting observation sample using principal component data, calculating the distance between damaged samples and undamaged samples, truss damage extent can be evaluated successfully. At the same time, some problems, which can not be solved very well only using the damage orientation method, also be solved using the damage distance mothed, so damage distance method is a very good supplement for truss damage orientation method.
Using twice measured data of the FRFs from undamaged truss, the minimal damage distance can be obtained. The minimal damage distance is a index for quickly judging truss damage in truss on-line health monitoring. In the other hand, the minimal damage distance can be used as a quantity unit for truss damage extent evaluation.
(4) The dynamic test signals obtained from practical truss have been contaminated by the noise, and existing truss has complicated boundary condition, big mass and damp, so the reliability of dynamic test signal noise is reduced. Therefore, a method for reducing or eliminating FRFs noise is proposed based on the PCA in the paper. By analyzing the PCA of original data matrix, we can reconstruct original data matrix using first several principal components, which generally contain all most information of original data. Thus, the original data noise can be reduced or eliminated, which is the basis for next damage identifications.
(5) In order to validate the reliability of the method, a whole size truss was tested with 20 kinds of damage case. The experimental result shows that the proposed method is feasible and reliable for truss damage identification. At the same time, the measurement points selection, exciting signal control and response signal collection, are also searched for the SISO dynamic test method, as well as testing process and result evaluation. In the last, the basic dynamic test methods and process with manual exciting manner are suggested and summarized in the paper.
The damage diagnosis method proposed in the paper directly uses FRFs for truss damage identification, does not need any modal parameters and integral modal data, so damage diagnosis results are not affected by modal errors and incomplete data. Since the damage diagnosis, which is performed by analyzing FRF data character, does not need truss mechanics mode, so it has not any special requirement for truss structure types, restricting manner and boundary condition. And the dynamic test method using manual excitation and SISO is simple and convenient. Therefore, the damage diagnosis method proposed in the paper has very important theoretical and practical value for health monitoring and damage diagnosis of existing truss.
引文
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